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Based on Takahashi-Umezawa thermo field dynamics and the order-invariance ofWeyl ordered operators under similar transformations, we present a new approachto deriving the exact Wigner functions of thermo number state, photonsubtracted and added thermo vacuum state. We find that these Wigner functionsare related to the Gaussian-Laguerre type functions of temperature, whosestatistical properties are then analysed.

Wigner functions of thermo number state, photon subtracted and added thermo vacuum state at finite temperature